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Abstract:

A method of aligning at least two wave shaping elements, a method of
measuring a deviation of an optical surface from a target shape and a
measuring apparatus for interferometrically measuring a deviation of an
optical surface from a target shape. The method of aligning at least two
wave shaping elements, each of which wave shaping elements has a
diffractive measurement structure for adapting part of a wave front of
incoming light to a respective portion of the target shape, includes:
providing a first one of the wave shaping elements with a diffractive
alignment structure, arranging the wave shaping elements relative to each
other such that each of the diffractive measurement structures is
traversed by a separate subset of rays of the incoming light during
operation of the measuring apparatus, and aligning the first wave shaping
element and a second one of the wave shaping elements relative to each
other by evaluating alignment light having consecutively interacted with
the diffractive alignment structure and with the second wave shaping
element.

Claims:

1. A method of aligning at least two wave shaping elements of a measuring
apparatus for interferometrically measuring a deviation of an optical
surface from a target shape, each of which wave shaping elements
comprises a diffractive measurement structure for adapting part of a wave
front of incoming light to a respective portion of said target shape,
said method comprising: providing a first one of said wave shaping
elements with a diffractive alignment structure, arranging said wave
shaping elements relative to each other such that each of said
diffractive measurement structures is traversed by a separate subset of
rays of said incoming light during operation of said measuring apparatus,
and aligning said first wave shaping element and a second one of said
wave shaping elements relative to each other by evaluating alignment
light having consecutively interacted with said diffractive alignment
structure and with said second wave shaping element.

2. The method according to claim 1, wherein said alignment light is light
from said incoming light.

3. The method according to claim 1, wherein said diffractive alignment
structure has at least two substructures, each of which substructures is
adapted to a separate optical wavelength.

4. A method of measuring a deviation of an optical surface from a target
shape, said method comprising: generating incoming light having a wave
front, providing at least two wave shaping elements, each having a
diffractive measurement structure for adapting part of said wave front to
a respective portion of said target shape, aligning said wave shaping
elements according to the method of claim 1, illuminating said optical
surface with said incoming light having traversed said diffractive
measurement structures and thereby generating measuring light having
interacted with said optical surface, and performing an interferometric
measurement by superimposing reference light with at least a portion of
said measuring light.

5. A method of measuring a deviation of an optical surface from a target
shape comprising: generating incoming light having a wave front,
providing at least two diffractive measurement structures, each for
adapting part of said wave front to a respective portion of said target
shape, and arranging said diffractive measurement structures relative to
each other such that each diffractive measurement structure is traversed
by a separate subset of rays of said incoming light, wherein each
diffractive measurement structure has a respective surface normal and
said surface normals are tilted relative to each other, illuminating said
optical surface with said incoming light having traversed said
diffractive measurement structures and thereby generating measuring light
having interacted with said optical surface, and performing an
interferometric measurement by superimposing reference light with at
least a portion of said measuring light.

6. A method of measuring a deviation of an optical surface from a target
shape comprising: generating incoming light having a wave front,
providing at least two diffractive measurement structures, each for
adapting part of said wave front to a respective portion of said target
shape and arranging said diffractive measurement structures relative to
each other such that each diffractive measurement structure is traversed
by a separate subset of rays of said incoming light, illuminating a first
area of said optical surface with said incoming light having traversed
said diffractive measurement structures and thereby generating first
measuring light having interacted with said first area, determining the
wave front of said first measuring light, designated as a first wave
front, by performing a first interferometric measurement, generating
second measuring light having interacted with at least a second area of
said optical surface, and determining the wave front of said second
measuring light, designated as a second wave front, by performing a
second interferometric measurement, and determining a deviation of said
optical surface from said target shape using a stitching algorithm, which
stitching algorithm includes determining misalignment components of said
at least two diffractive measurement structures based on said first wave
front and said second wave front.

Description:

[0001] This application is a Divisional of U.S. application Ser. No.
12/684,600, filed on Jan. 8, 2010, which is a continuation of
International Patent Application PCT/EP2008/005548, filed on Jul. 8,
2008, and claiming priority from International Patent Application
PCT/EP2007/006069, filed on Jul. 9, 2007. The complete disclosures of
these patent applications are incorporated into this application by
reference.

FIELD OF AND BACKGROUND OF THE INVENTION

[0002] The present invention relates to a method of aligning at least two
wave shaping elements of a measuring apparatus for interferometrically
measuring a deviation of an optical surface from a target shape. Further,
the invention relates to a method of measuring a deviation of an optical
surface from a target shape, a method of manufacturing an optical element
having an optical surface of an aspherical target shape. Additionally,
the present invention relates to large aspheres or small aspheres having
a large numerical aperture.

[0003] An optical surface to be measured can be the surface of an optical
lens element or an optical mirror used in optical systems. Such optical
systems can e.g. be configured as telescopes used in astronomy, and
systems used for imaging structures, such as structures formed on a mask
or a reticle, onto a radiation sensitive substrate, such as resist, by a
lithographic method. The quality of such optical systems is substantially
determined by the accuracy with which the optical surface can be machined
or manufactured to have a target shape determined by a designer of the
optical system. In such manufacturing it is necessary to compare the
actual shape of the machined optical surface with its target shape and to
determine differences between the machined and the target surfaces. The
optical surface may then be further machined especially at those portions
where differences between the machined and target surfaces exceed, for
example, predefined thresholds.

[0004] Interferometric measuring apparatuses are commonly used for high
precision measurements of optical surfaces. Examples of such apparatuses
are disclosed in WO2005/114101. The entire content of this document is
incorporated herein by reference.

[0005] An interferometric measuring apparatus for measuring a spherical
optical surface typically includes a source of sufficiently coherent
light and interferometer optics for generating a beam of measuring light
incident on the surface to be tested, such that wave fronts of the
measuring light have, at a position of the surface to be tested, the same
shape as the target shape of the surface under test. In such a situation,
the beam of measuring light is orthogonally incident on the surface under
test, and is reflected therefrom to travel back towards the
interferometer optics. Thereafter, the light of the measuring beam
reflected from the surface under test is superimposed with light
reflected from a reference surface and deviations between the shape of
the surface under test and its target shape are determined from a
resulting interference pattern.

[0006] While spherical wave fronts for testing spherical optical surfaces
may be generated with a relatively high precision by conventional
interferometer optics, more advanced optics, such as computer generated
holograms (CGH's) are mostly necessary to generate beams of measuring
light having an aspherical wave front such that the light is orthogonally
incident at each location of an aspherical surface under test.

[0007] However, the size of CGH's available is limited, which in return
limits the size of the aspherical optical surfaces testable with high
accuracy, in particular if the optical surface is convex or raised.

SUMMARY OF THE INVENTION

[0008] It is an object of the invention to solve the above-mentioned
problems and in particular provide a method and a measuring apparatus by
means of which the deviation of an actual shape of an optical surface
from a target shape can be measured with high accuracy for large optical
surfaces.

[0009] This object is solved according to the invention by providing a
method of aligning at least two wave-shaping elements of a measuring
apparatus for interferometrically measuring a deviation of an optical
surface from a target shape, each of which wave shaping elements
comprises a diffractive measurement structure for adapting part of a wave
front of incoming light to a respective portion of the target shape,
which method comprises the steps of: providing a first one of the
wave-shaping elements with a diffractive alignment structure, arranging
the wave shaping elements relative to each other such that each of the
diffractive measurement structures is traversed by a separate subset of
rays of the incoming light during operation of the measuring apparatus,
and aligning the first wave shaping element and a second one of the wave
shaping elements relative to each other by evaluating alignment light
having consecutively interacted with the diffractive alignment structure
and with the second wave shaping element.

[0010] The object is further solved according to the invention by
providing a method of measuring a deviation of an optical surface from a
target shape, which method comprises the steps of: generating incoming
light having a wave front, providing at least two wave shaping elements,
each having a diffractive measurement structure for adapting part of the
wave front to a respective portion of the target shape, aligning the wave
shaping elements according to the above-mentioned alignment method,
illuminating the optical surface with the incoming light having traversed
the diffractive measurement structures and thereby generating measuring
light having interacted with the optical surface, and performing an
interferometric measurement by superimposing reference light with at
least a portion of the measuring light. Based on the interferometric
measurement a deviation of the optical surface from the target shape can
be determined. Further, the object is solved according to the invention
by providing a method of manufacturing an optical element having an
optical surface of an aspherical target shape, the method comprising the
steps of: measuring a deviation of the optical surface according to the
above-mentioned method and processing the optical surface based on the
measured deviation.

[0011] The above-mentioned object is further solved by providing a
measuring apparatus for interferometrically measuring a deviation of an
optical surface from a target shape. The measurement apparatus according
to the invention comprises means for generating incoming light having a
wave front, at least two wave shaping elements, each having a diffractive
measurement structure for adapting part of the wave front to a respective
portion of the target shape, which wave shaping elements are arranged
relative to each other such that each of the diffractive measurement
structures is traversed by a separate subset of rays of the incoming
light during operation of the measuring apparatus, wherein a first one of
the wave shaping elements comprises a diffractive alignment structure
adapted for aligning the first wave shaping element and a second one of
the wave shaping elements relative to each other by evaluating alignment
light having consecutively interacted with the diffractive alignment
structure and with the second wave shaping element. In an embodiment
according to the invention the measuring apparatus is adapted for
illuminating the optical surface with the incoming light having traversed
the diffractive measurement structures and thereby generating measuring
light having interacted with the optical surface, and the measuring
apparatus further comprises means for performing an interferometric
measurement by superimposing reference light with at least a portion of
the measuring light.

[0012] The incoming light according to the invention can be generated by
an illumination beam of one interferometer or by respective illumination
beams of several interferometers. The wavelength of the incoming light
can be in the visible or in the non visible wavelength range, for example
in a UV-wavelength range. The diffractive measurement structures are, as
mentioned above, configured to adapt part of the wave front of the
incoming light to a respective portion of the target shape. That means,
the incoming light is adapted such that it is orthogonally incident on
the optical surface in an extended region thereof, in case the optical
surface has its target shape.

[0013] By using diffractive measurement structures, such as holograms like
computer generated holograms (CGH's), for adapting the wave front of the
incoming light, an optical surface having an aspherical target shape can
be measured. The diffractive alignment structure provided on a first wave
shaping element can also comprise a CGH. The diffractive pattern of the
diffractive alignment structure differs from the diffractive patterns of
the diffractive measurement structures. In an embodiment of the invention
the diffractive alignment structure is further locally separated from the
diffractive measurement structure of the respective wave shaping element.

[0014] According to the invention, the wave shaping elements are arranged
relative to each other such that each of the diffractive measurement
structures is traversed by a separate subset of rays of the incoming
light during operation of the measuring apparatus. That means, there is a
portion of the incoming light, which traverses the first wave shaping
element but not the second wave shaping element and there is another
portion of the incoming light which traverses the second wave shaping
element but not the first wave shaping element. The wave shaping elements
can be arranged in order to overlap or not to overlap in projection along
the propagation direction of the incoming light. Put in different words,
the wave shaping elements are arranged adjacent to each other with
respect to the propagation direction of the incoming light. In an
embodiment the wave shaping elements are arranged in a single plane or in
different planes transverse to the propagation direction of the incoming
light.

[0015] According to the invention, the first wave shaping element and the
second wave shaping element are aligned relative to each other by
evaluating alignment light having consecutively interacted with the
diffractive alignment structure and the second wave shaping element.
Therefore, the alignment light first interacts with the diffractive
alignment structure and after that with the second wave shaping element.
Therefore, the wave shaping elements are aligned directly to each other,
i.e. not via a third element, such as via the optical surface or via an
optical element of the measuring apparatus. The interferometric
measurement is performed by superimposing reference light with at least a
portion of the measuring light and can be performed by different
interferometric methods known in the art. Suitable interferometer systems
can be of the Fizeau or the Twyman-Green type, examples of which are
illustrated in Chapter 2.1 of the text book edited by Daniel Malacara,
Optical Shop Testing, Second Edition, Wiley Interscience Publication
(1992). Also a Michelson-Type interferometer and any other suitable type
of interferometer may be used.

[0016] By aligning the first wave shaping element and the second wave
shaping element according to the invention by evaluating alignment light
having consecutively interacted with the diffractive alignment structure
and the second wave shaping element, the wave fronts adapted by the
respective diffractive measurement structures match each other
particularly well. This allows the measurement of the deviations of an
optical surface being larger than the size of a single diffractive
measurement structure, such as a CGH, in particular having a convex
shape, from its target shape with high accuracy.

[0017] As according to the invention the alignment is performed by
evaluating alignment light having consecutively interacted with the
diffractive alignment structure and the second wave shaping element, the
wave shaping elements are aligned directly to each other. This leads to a
more precise alignment compared to individual alignments of the wave
shaping elements to a third element.

[0018] In an embodiment of the alignment method according to the invention
the alignment light is light from the incoming light. According to this
embodiment part of the incoming light is used as alignment light and
another part of the incoming light is sent via the diffractive
measurement structures onto the optical surface. In a further embodiment
the incoming light has a spherical wave front. The incoming light can
e.g. be generated by a light source producing a plane wave and a
pre-shaping optical element transforming the same into a spherical wave.

[0019] In a further embodiment of the invention the diffractive alignment
structure focuses the alignment light onto a reflective surface of the
second wave shaping element. Thereby the diffractive alignment structure
generates a converging auxiliary wave, for example having a spherical
wave front, being focused onto the reflective surface. This focussing
condition is also referred to as cat-eye focus. The reflected light can
be used for determining the distance between the two wave shaping
elements in a direction of the incoming light, which is typically
parallel to the optical axis of the measuring apparatus.

[0020] In a further embodiment according to the invention the diffractive
alignment structure comprises a hologram, in particular a computer
generated hologram (CGH). Such a hologram allows a manipulation of the
wave front of the alignment light in a suitable way in order to optimise
the alignment process.

[0021] In a further embodiment according to the invention the diffractive
alignment structure has at least two substructures, each of which
substructure is adapted to a separate optical wavelength. Advantageously
the substructures are configured such that alignment light for each of
the separate optical wavelengths is adapted by the diffractive alignment
structure to the same wave. Therefore, the alignment between the two wave
shaping elements can be performed in the same manner for each of the
separate optical wavelengths. This way the measurement structures of the
wave shaping elements can be easily operated with different optical
wavelengths of the incoming light. In particular, the optical wavelengths
can be selected such that for a first optical wavelength the diffractive
measurement structures create a wave front adapted to a first optical
surface, and for a second optical wavelength of the incoming light the
diffractive measurement structures adapt the wave front to a second
optical surface. For that purpose the diffractive measurement structures
can e.g. be double coded and therefore contain two substructures, each of
which is adapted to one of the optical wavelengths.

[0022] The diffractive alignment structures having two substructures,
according to this embodiment, can be operated using the incoming light of
the different wavelengths as alignment light.

[0023] According to a further embodiment each of the wave shaping elements
is provided with a diffractive alignment structure and the wave shaping
elements are aligned relative to each other using each of the diffractive
alignment structures. In this way a particularly precise alignment
between the wave shaping elements can be obtained.

[0024] In a further embodiment according to the invention the diffractive
alignment structure generates an auxiliary wave, which is directed at a
further diffractive alignment structure provided on the second wave
shaping element. The light of the auxiliary wave having interacted with
the further diffractive alignment structure allows the relative alignment
between the two wave shaping elements to be determined with a high degree
of accuracy. In an embodiment the auxiliary wave has a non-plane wave
front. Therefore, the auxiliary wave is either a diverging or a
converging wave, wherein the wave front can be, for example, spherical.

[0025] In a further embodiment according to the invention the further
diffractive alignment structure provided on the second wave shaping
element acts as a Littrow grating. As is known in the art, a Littrow
grating is configured such that a wave reflected by the Littrow grating
travels back within itself. The light of the auxiliary wave reflected
back from the Littrow grating can be used to determine both the distance
between the two wave shaping elements with respect to the propagation
direction of the incoming light as well as the relative position of the
two wave shaping elements in a lateral direction with respect to the
propagation direction of the incoming light. This alignment information
can be obtained by superimposing the reflected light of the auxiliary
wave with reference light of the measuring apparatus and evaluating the
resulting interferogram. In other words, according to this embodiment of
the invention, both the axial distance and the decentration of the two
wave shaping elements can be determined relative to each other.

[0026] In a further embodiment according to the invention the diffractive
alignment structure generates a plane auxiliary wave having a propagation
direction, which is tilted with respect to the direction of the
propagation direction of the incoming light. This way, the decentration
between the two wave shaping elements being the relative position between
the two wave shaping elements in a lateral direction with respect to the
propagation direction of the incoming light can be measured with a high
accuracy. The tilt of the plane auxiliary wave with respect to the
propagation direction of the incoming light can for example be in the
area of 25°. In another embodiment the auxiliary wave is also
directed onto a further diffractive alignment structure provided on the
second wave shaping element acting as a Littrow grating. It is
furthermore advantageous, if the diffractive alignment structure further
focuses light on a reflective surface of the second wave shaping element
in a cat-eye fashion in order to determine the axial distance between the
two wave shaping elements.

[0027] In a further embodiment according to the invention the first wave
shaping element comprises a second alignment structure, in particular a
diffractive alignment structure, for aligning the tilt of the first wave
shaping element relative to a propagation direction of the incoming
light. In other words, the second alignment structure has the function of
adjusting the tilt angle of a surface normal on the wave shaping element
with respect to the propagation direction of the incoming light or the
optical axis of the measuring apparatus. Advantageously, the second
alignment structure comprises a Littrow grating. In a further embodiment
the second wave shaping element also comprises an alignment structure for
aligning the tilt of the second wave shaping element relative to a
propagation direction of the incoming light. Advantageously, this
alignment structure is also a diffractive alignment structure comprising
a Littrow grating

[0028] In a further embodiment according to the invention, the incoming
light has a propagation direction and the wave shaping elements are
offset from each other in the propagation direction. In other words, the
wave shaping elements are placed in a cascaded arrangement along the
propagation direction. Further the wave shaping elements are laterally
shifted relative to each other. In this arrangement an alignment of the
wave shaping elements relative to each other can be conducted with a
particularly high accuracy.

[0029] According to a further embodiment of the invention, the wave
shaping elements are arranged such that adjacent wave shaping elements
overlap in projection along the propagation direction. In other words,
the wave shaping elements are arranged such that there is an overlapping
area between the wave shaping elements in which rays from the incoming
light would have to pass both wave shaping elements in order to pass on
to the optical surface. In this arrangement the relative alignment
between the wave shaping elements can be achieved with a particularly
high accuracy using the diffractive alignment structure according to the
invention.

[0030] In a further embodiment according to the invention the wave shaping
elements are aligned relative to each other with a tolerance of less than
100 nm. This tolerance applies both in axial and lateral directions of
alignment with respect to the optical axis of the measuring apparatus.

[0031] The above object is further solved according to the invention by
providing a method of measuring a deviation of an optical surface from a
target shape comprising the steps of generating incoming light having a
wave front, providing at least two diffractive measurement structures,
each for adapting part of the wave front to a respective portion of the
target shape, and arranging the diffractive measurement structures
relative to each other such that each diffractive measurement structure
is traversed by a separate subset of rays of the incoming light, wherein
each diffractive measurement structure has a respective surface normal
and the surface normals are tilted relative to each other, illuminating
the optical surface with the incoming light having traversed the
diffractive measurement structures and thereby generating measuring light
having interacted with the optical surface, performing an interferometric
measurement by superimposing reference light with at least a portion of
the measuring light, and determining a deviation of the optical surface
from the target shape based on the interferometric measurement.

[0032] The above object is further solved by a method of manufacturing an
optical element having an optical surface of an aspherical target shape,
which method comprises the steps of: measuring a deviation of the optical
surface according to the above method of measuring a deviation of an
optical surface from a target shape, and processing the optical surface
based on the measured deviation.

[0033] The above object is further solved by a measuring apparatus for
measuring a deviation of an optical surface from a target shape, which
measuring apparatus comprises means for generating incoming light having
a wave front, at least two diffractive measurement structures, each for
adapting part of the wave front to a respective portion of the target
shape, which diffractive measurement structures are arranged relative to
each other such that each of the diffractive measurement structures is
traversed by a separate subset of rays of the incoming light during
operation of the measuring apparatus, wherein each diffractive
measurement structure has a respective surface normal and the surface
normals are tilted relative to each other, which measuring apparatus is
adapted for illuminating the optical surface with the incoming light
having traversed the diffractive measurement structures and thereby
generating measuring light having interacted with the optical surface,
and which measuring apparatus further comprises means for performing an
interferometric measurement by superimposing reference light with at
least a portion of the measuring light. From the interferometric
measurement a deviation of the optical surface from the target shape can
be determined. Advantageously, the measuring apparatus further comprises
means for determining such a deviation of the optical surface from the
target shape based on the interferometric measurement.

[0034] In other words, according to the invention the diffractive
measurement structures are tilted relative to each other. The tilt
between the surface normals of the diffractive measurement structures is
advantageously at least 1°, in one embodiment, according to the
invention, between 20° and 90°.

[0035] The method according to the invention of tilting the surface
normals of the measurement structures relative to each other allows a
convex or raised optical surface to "immerse" into the diffractive
measurement structures. The tilted diffractive measurement structures
approximate the shape of a convex optical surface better than diffractive
measurement structures arranged in the same plane. Therefore, the area of
the optical surface to be measured can be moved closer to the diffractive
measurement structures if the surface normals are tilted relative to each
other. This allows a larger optical surface to be measured using
diffractive measurement structures of a given size.

[0036] In case a convex optical surface of a size larger than the size
measurable by two diffractive measurement structures arranged in a plane
needs to be measured, the method according to the invention improves the
measurement accuracy obtainable. That is, as according to the inventive
solution the use of more than two diffractive measurement structures can
be avoided, which would cause larger alignment uncertainties of the
diffractive measurement structures relative to each other than in the
case of only two diffractive measurement structures. By arranging the
diffractive measurement structures with tilted surface normals according
to the invention, the given optical surface can possibly be measured
using only two diffractive measurement structures, which in return
reduces the overall alignment inaccuracies. This leads to a more accurate
measurement result of the deviations of the optical surface.

[0037] In a further embodiment according to the invention the surface
normals are tilted such that the wave shaping elements form a roof-shaped
structure, which is adapted such that the optical surface having a convex
shape can at least partly be inserted therein. In this way the average
distance between the optical surface to be measured and the diffractive
measurement structures can be reduced allowing the measurement of a
larger optical surface.

[0038] In a further embodiment according to the invention the incoming
light comprises two separate light beams, each of which propagates along
a respective surface normal of the diffractive measurement structures.
Therefore, the light beams are tilted relative to each other as are the
surface normals of the diffractive measurement structures. According to
this embodiment the propagation directions of the respective light beams
do not have to be deviated as much by the diffractive measurement
structures, which allows a more accurate measurement of the surface
deviation. In a further embodiment, the separate light beams are the
illumination beams of separate interferometers.

[0039] A further embodiment of the measuring method according to the
invention includes the following steps: illuminating a first area of the
optical surface with the incoming light having traversed the diffractive
measurement structures and thereby generating first measuring light
having interacted with the first areas, generating second measuring light
having interacted with at least a second area of the optical surface and
determining the wave front of the second measuring light, designated as a
second wave front, by performing a second interferometric measurement,
and determining the deviation of the optical surface from the target
shape based on the first and the second interferometric measurements. In
this way, an optical surface of an increased size can be measured using a
given number of wave shaping elements. Further embodiments relating to
determining the deviation of the optical surface from the target shape
based on the first and the second interferometric measurements are
illustrated hereinafter.

[0040] The above-mentioned object is further solved according to the
invention by a method of measuring a deviation of an optical surface from
a target shape comprising the steps of: generating incoming light having
a wave front, providing at least two diffractive measurement structures,
each for adapting part of the wave front to a respective portion of the
target shape and arranging the diffractive measurement structures
relative to each other such that each of the diffractive measurement
structures is traversed by a separate subset of rays of the incoming
light, illuminating a first area of the optical surface with the incoming
light having traversed the diffractive measurement structures and thereby
generating first measuring light having interacted with the first area,
determining the wave front of the first measuring light, designated as a
first wave front, by performing a first interferometric measurement,
generating second measuring light having interacted with at least a
second area of the optical surface, and determining the wave front of the
second measuring light, designated as a second wave front, by performing
a second interferometric measurement, determining a deviation of the
optical surface from the target shape using a stitching algorithm, which
stitching algorithm includes: determining misalignment components of the
at least two diffractive measurement structures based on the first wave
front and the second wave front. The second area is different from the
first area but can overlap with the first area.

[0041] The above object is further solved by a method of manufacturing an
optical element having an optical surface of an aspherical target shape,
wherein the method comprises the steps of measuring a deviation of the
optical surface according to the aforementioned method, and processing
the optical surface based on the measured deviation.

[0042] Further, the above object is solved by a measuring apparatus for
measuring a deviation of an optical surface from a target shape which
measuring apparatus comprises: means for generating incoming light having
a wave front, at least two diffractive measurement structures, each for
adapting part of the wave front to a respective portion of the target
shape, which wave shaping elements are arranged relative to each other
such that each diffractive measurement structure is traversed by a
separate subset of rays of the incoming light during operation of the
measuring apparatus, which measuring apparatus is adapted for
illuminating first areas of the optical surface with the incoming light
having traversed the diffractive measurement structures, thereby
generating measuring light having interacted with the first areas of the
optical surface, and generating second measuring light having interacted
with at least a second area of the optical surface, and which measuring
apparatus further comprises: means for performing a first interferometric
measurement for determining the wave front of the first measuring light,
means for performing a second interferometric measurement for determining
the wave front of the second measuring light, designated as a second wave
front, and means for determining a deviation of the optical surface from
the target shape using a stitching algorithm, which stitching algorith
includes determining misalignment components of the at least two
diffractive measurement structures based on the first wave front and the
second wave front.

[0043] By determining the misalignment components of the at least two wave
shaping elements based on the first wave front and the second wave front
according to the invention, the misalignment components can be accounted
for by the stitching algorithm when stitching the first wave front and
the second wave front together. In an embodiment according to the
invention, the deviation of the optical surface from the target shape is
determined based on the first wave front, the second wave front and the
misalignment components. By virtue of the stitching algorithm, according
to the invention, the wave shaping elements only have to be roughly
aligned before determining the wave fronts. The alignment only has to be
performed such that the first wave front and the second wave front are
arranged in a way, in which a continuous wave front can be measured. The
second area advantageously abuts to the first area such that stitching
between the respective wave fronts can be performed. The stitching
algorithm according to the invention allows a very precise measurement of
the deviation of the optical surface from its target shape, as possible
misalignments between the two diffractive measurement structures are
compensated for by the stitching algorithm. Further, complex and costly
alignment procedures become unnecessary for measuring the optical
surface.

[0044] The incoming light used for measuring the deviation of the optical
surface can be generated by the illumination beam of a single
interferometer or can be composed from respective illumination beams of
several interferometers. The interferometric measurements are conducted
by respectively superimposing the measuring light with reference light,
as also detailed above. The determined wave front deviations correspond
to deviations of the optical surface from its target shape in the
respective areas. Determining a wave front of the respective measuring
light according to the invention is to be understood as either
determining the actual shape of the wave front or the shape of a
deviation distribution of the respective wave front from the wave front
of the reference light.

[0045] In an embodiment according to the invention the first area
comprises at least two separate sub areas having a gap in between and the
second area covers this gap. For example, the two wave shaping elements
can be arranged in an overlapping fashion such that the light traversing
the wave shaping elements in the non overlapping area interacts with the
two separate subareas of the first area. The area of the optical surface
corresponding to the overlapping section of the wave shaping elements is
then measured in a second measurement step using the second measuring
light. Advantageously the determining of the deviation of the optical
surface includes determining respective deviation distributions for the
first and the second areas from the first and the second interferometric
measurements, respectively, and mathematically stitching the deviation
distributions together to obtain an overall deviation distribution. The
overall deviation distribution covers the whole area of the first and the
second areas of the optical surface.

[0046] In a further embodiment according to the invention the target shape
of the optical surface is rotationally symmetric with respect to an
attributed axis of symmetry, the first interferometric measurement is
performed with the optical surface being arranged in a first rotational
position and the second interferometric measurement is performed with the
optical surface being arranged in a second rotational position different
from the first rotational position. In one embodiment the axis of
symmetry of the optical surface extends parallel to the propagation
direction of the incoming light. Alternatively, the axis of symmetry
extends laterally with respect of the propagation direction. In both
embodiments the same wave shaping elements can be used for the first and
the second interferometric measurements. In order to arrange the optical
surface in the different rotational positions, it is advantageous if a
pivot bearing is provided for rotating the test object comprising the
optical surface. This way different sub-apertures on the optical surface
can be measured.

[0047] In a further embodiment according to the invention, the first
interferometric measurement is performed using a first set of diffractive
measurement structures and the second interferometric measurement is
performed using a second set of diffractive measurement structures, which
second set of diffractive measurement structures is shifted with respect
to the first set of diffractive measurement structures and has
correspondingly adapted diffractive measurement structures. In other
words, the diffractive measurement structures of the first set of
diffractive measurement structures are adapted to shape the wave front of
the incoming light to match the target shape in the first area of the
optical surface and the diffractive measurement structures of the second
set of diffractive measurement structures are adapted to the target shape
in the second area of the optical surface. In this way, a large optical
surface can be measured, even if it is not symmetric. Therefore a
so-called free form surface of large size can be measured according to
this embodiment.

[0048] In a further embodiment of the invention the determined
misalignment components include alignment offsets of each diffractive
measurement structure, which alignment offsets include an offset value
for each degree of freedom in alignment of the respective diffractive
measurement structure. Each diffractive measurement structure can, for
example, have 6 degrees of freedom in alignment such as tilt in two
directions, decentration of the diffractive measurement structure in two
lateral directions with respect to the optical axis of the measuring
apparatus, the azimuthal angle with respect to the optical axis and the
distance of the wave shaping element from the optical surface. In case of
linear dependence between single degrees of freedom, the offset values
can be reduced correspondingly.

[0049] In a further embodiment, according to the invention, the
determining of the misalignment components includes determining a
sensitivity distribution (Bkl)x,y for each wave shaping element
which sensitivity distribution (Bkl)x,y describes the influence
of a given misalignment of a respective diffractive measurement structure
k in a respective degree of freedom l on the first wave front as a
function of coordinates x and y in a projection plane perpendicular to a
propagation direction of the first measuring light and minimising a
mathematical term including the following expression:

l = 1 Af b kl ( B kl ) x , y , ( 1 )
##EQU00001##

wherein bkl is a respective misalignment coefficient of a respective
diffractive measurement structure k and a respective degree of freedom l,
and Af is the number of degrees of freedom in alignment of the
diffractive measurement structures. In a further embodiment of the
invention the expression (1) is subtracted from the first wave front and
the result included squared in the mathematical term to be minimised.

[0050] In a further embodiment according to the invention, at least one of
the sensitivity distributions (Bkl)x,y can be expressed by
several other sensitivity distributions (Bkl)x,y. That means, a
certain type of misalignment, for example a tilt, of a given diffractive
measurement structure, causes the same effect to the resulting wave
front, for example the appearance of coma, as does a linear combination
of other misalignment components of the given diffractive measurement
structure. Often the azimuth sensitivity distribution can be described by
a linear combination of tilt and decentring sensitivity distributions. In
case at least two sensitivity distributions being linearly dependent on
each other, the number of alignment offsets to be determined by the
measurement method according to the invention, is reduced.

[0051] In an embodiment according to the invention, the misalignment
coefficients bkl are fitting coefficients determined from a least
square calculation.

[0052] Advantageously the determining of the misalignment components
includes determining a sensitivity distribution Ajk,y of the optical
surface describing the influence of a given misalignment of the optical
surface in a respective degree of freedom j on the first wave front as a
function of the coordinates x and y, and minimizing a mathematical term
including the following expression:

j = 1 AJ [ a mj - a nj ] A jx , y , ( 2 )
##EQU00002##

wherein amj and anj are respective misalignment coefficients of
the optical surface for respective rotational positions m and n and AJ is
the number of degrees of freedom in alignment of the optical surface.
Typical degrees of freedom in alignment of the optical surface include
tilt in two directions with respect to the optical axis of the measuring
apparatus, decentration in two lateral directions with respect to the
optical axis and the distance of the diffractive measurement structure
with respect to the optical surface. By including the expression (2) into
the mathematical term to be minimised, the misalignment components of the
optical surface can be properly accounted for in the stitching algorithm.

[0053] In a further embodiment according to the invention, prior to
performing the first interferometric measurement the distance between one
of the diffractive measurement structures, acting as a reference element,
and the optical surface is adjusted. In an embodiment of the invention,
the wave shaping element acting as a reference element is a central wave
shaping element which is arranged such that the light from the incoming
light traversing the central wave shaping element illuminates the optical
surface in a central region, in particular in an area of an axis of
symmetry. Performing the above-mentioned adjustment in distance between
the reference element and the optical surface allows misalignment
components of the diffractive measurement structures to be determined
subsequently in a particularly precise manner using the stitching
algorithm.

[0054] In a further embodiment according to the invention, prior to
performing the first interferometric measurement the diffractive
measurement structures are roughly aligned such that a continuous wave
front of the first measuring light can be measured during the first
interferometric measurement. Advantageously, the rough alignment is done
such that half of the period of an interference pattern generated by the
first measuring light and the reference light covers at least two pixels
of a detector recording the interference pattern. Advantageously, each of
the diffractive measurement structures is mounted on an alignment device.
In an embodiment of the alignment device, the respective diffractive
measurement structure can be adjusted in 6 degrees of freedom
(decentration x, decentration y, tilt x, tilt y, azimuth angle and
distance z, wherein the optical axis of the measurement apparatus extends
along z).

[0055] In a further embodiment, according to the invention, the alignment
includes at least one of the steps: roughly aligning a first diffractive
measurement structure acting as a reference element with respect to
another component of the measuring apparatus, adjusting the distance of
the reference element with respect to the optical surface, and roughly
aligning at least one other diffractive measurement structure. The
distance of the reference element with respect to the optical surface
can, for example, be adjusted using a cat-eye auxiliary grating on the
wave shaping element carrying the diffractive measurement structure or
using optical coherence tomography (OCT), a Littrow grating or an
autocollimator etc. The alignment of the at least one other diffractive
measurement structure can be performed with respect to another component
of the measuring apparatus or with respect to the optical surface.

[0056] It is a further object of the invention to provide an asphere
having improved properties. This object is solved, according to the
invention, by an asphere having an aspherical optical surface extending
over a diameter D of the asphere, wherein a best fitting spherical
surface of the aspherical optical surface has a radius of curvature R,
and the parameters D and R are related as follows:

D > 2 R sin ( arctan 500 mm 2 R
) ( 3 ) ##EQU00003##

[0057] The manufacture of such an asphere is made possible by the
manufacturing method according to the invention. Currently available
CGH's have a diameter of less than 300 mm. An aspherical optical surface
having parameters satisfying the relation (3) cannot be measured properly
using a single CGH. This is even not possible, if the optical surface is
rotationally symmetric, the optical surface is measured in different
rotational positions and the results are stitched together.

[0058] In case, in which the aspherical optical surface is convex, the
light emanating from the CGH converges towards the optical surface.
Therefore, in order to measure such a convex surface using a single CGH a
CGH having a diameter larger than 300 nm would be required. Also in the
case, in which the radius of curvature R is very large relative to the
diameter of a CGH, i.e. the aspherical optical surface extends
essentially along a plane, the size of currently available CHG's is not
sufficient to measure the optical surface using a single CGH.

[0059] In the case, in which the aspherical optical surface is concave,
the light emanating from the CGH diverges towards the optical surface.
The measurement of an asphere having the above parameters by means of a
single CGH would require the CGH to be arranged a large distance away
from the optical surface. That is, as in close proximity to such a
concave aspherical optical surface single rays of the measuring light
intersect with each other. If the CGH was located in this area, the
measurements would be indeterminate. Therefore, the CGH has to be located
outside of this area. According to a first option the CGH can be located
in very close proximity to the optical surface, which would require the
CGH to be larger than currently available, in order to measure the entire
optical surface. According to another option, the CGH can be located in
an area far away from the optical surface, in which the single rays of
the measuring light do not intersect. In this arrangement, however, the
measurement accuracy is reduced to an inacceptable level.

[0060] An optical surface being characterized by (3) can however be
measured by the above measuring method according to the invention using
at least two diffractive measurement structures in form of e.g. CGH's.

[0061] In a further embodiment according to the invention, D and R are
related as follows:

D > 2 R sin ( arctan 600 mm 2 R
) ( 4 ) ##EQU00004##

[0062] Advantageously, the asphere is produced by the above-mentioned
method of manufacturing an optical element according to the invention.

[0063] The object is further solved by providing an asphere having an
aspherical optical surface extending over a diameter D of the asphere,
wherein a best fitting spherical surface of the aspherical optical
surface has a radius of curvature R of at least 130 mm and the ratio D/R
is larger than 1.3. In another embodiment the ratio D/R is larger than
1.5, especially larger than 2.0. Advantageously, the asphere is also
produced by the above method of manufacturing an optical element
according to the invention.

[0064] The best fitting spherical surface of the aspherical optical
surface is advantageously convex. As detailed above, this also includes a
best fitting surface of plane shape, if the radius of curvature R becomes
very large. In the case, in which the best fitting surface is plane, the
aspherical optical surface can comprise subareas of convex and concave
shapes next to each other. In an alternate embodiment the best fitting
spherical surface of the aspherical optical surface is concave.

[0065] In an embodiment of the asphere according to the invention, the
diameter D is larger 500 mm, advantageously larger than 600 mm. According
to a further embodiment of the invention, the optical surface is
rotationally symmetric with respect to an axis of symmetry.

[0066] Such a rotationally symmetric asphere may be represented by the
following formula, which is known to the person skilled in the art as
"asphere-equation":

[0067] In this equation z represents the z-coordinate of the surface of
the target shape at a distance r from the optical axis or axis of
symmetry, c is the curvature of the aspherical surface, k is the conic
coefficient, and αi are further coefficients. An exemplary
embodiment of the target shape is characterized by the following
parameters for the above equation:

[0069] In a further embodiment of the asphere, the optical surface is
rotationally non-symmetric and the diameter D is larger than 300 mm. In
case the optical surface has the shape of an ellipse according to this
embodiment the largest diameter D is larger than 300 mm. The optical
surface according to this embodiment can also be referred to as a free
form surface. In this case, measuring the surface in different rotational
positions using the same CGH is not possible. Therefore only the
measuring method according to the invention using at least two
diffractive measurement structures allows the measurement of an asphere
of the above embodiment with sufficient accuracy. A free form surface may
be represented by different mathematical functions, for example splines
or simple xy-polynomials in the following form:

z = n , m a nm x n y m ##EQU00006##

wherein z is the arrow height and n+m≦10 or ≦20. Such
representations are supported by many optical design programs like Code V
known to the person skilled in the art.

[0070] According to a further embodiment, the optical surface has a
deviation from the best fitting spherical surface of at least 50 μm,
in particular at least 100 μm. Aspherical optical surfaces having a
deviation from the best fitting spherical surface of less than 100 μm
are referred to as weak or mild aspheres which can often be measured with
respect to their deviation from their target shape using spherical
optical elements instead of diffractive measurement structures. According
to a further embodiment, the optical surface has a deviation from the
best fitting spherical surface of at least 200 μm.

[0071] In a further embodiment according to the invention the asphere is
manufactured to a tolerance sufficient for microlithographic
applications, in particular the actual shape of the optical surface
deviates from a target shape of the optical surface by a maximum of 1
μm. The manufacture of an asphere having the above mentioned
characteristics and having this tolerance is made possible by the
manufacturing method according to the invention.

[0072] In a further embodiment according to the invention, the asphere has
two convex optical surfaces, each being shaped aspherically. The ashpere,
according to this embodiment, can also be referred to as a
double-asphere. The parameters D and R of each of the two aspherical
optical surfaces preferably meet the requirements set forth above with
regards to the aspherical optical surface, in particular the requirements
contained in equations (3) and (4).

[0073] According to the invention, further an arrangement of a multitude
of the above-mentioned ashperes is provided wherein the actual shapes of
the optical surfaces of the respective aspheres deviate from each other
by a maximum of 5 μm. Such aspheres are suitable for use in
microlithographic exposure tools due to their tight surface tolerances
over a large diameter.

[0074] According to the invention, further a projection objective of a
projection exposure tool for microlithography is provided, which
projection objective comprises at least one of the above aspheres
according to the invention. In one embodiment the projection objective is
configured for operation with extreme ultraviolet light (EUV).

[0075] The features specified above with respect to the method according
to the invention can be transferred correspondingly to the measuring
apparatus according to the invention. Advantageous embodiments of the
measuring apparatus according to the invention resulting therefrom shall
also be covered by the disclosure of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

[0076] The foregoing, as well as other advantageous features of the
invention, will be more apparent from the following detailed description
of exemplary embodiments of the invention with reference to the following
diagrammatic drawings, wherein:

[0077]FIG. 1 illustrates a measuring apparatus for interferometrically
measuring a deviation of an optical surface from a target shape according
to a first embodiment of the invention;

[0078]FIG. 2 illustrates a portion of a measuring apparatus for
interferometrically measuring a deviation of an optical surface from a
target shape according to a further embodiment of the invention;

[0079]FIG. 3 illustrates a portion of a measuring apparatus for
interferometrically measuring a deviation of an optical surface from a
target shape according to a further embodiment of the invention;

[0080]FIG. 4 illustrates optical effects related to measuring a deviation
of a concave aspherical optical surface from a target shape;

[0081]FIG. 5 illustrates a portion of the measuring apparatus according
to FIG. 1 including a set of two wave shaping elements in a first
embodiment;

[0082]FIG. 6 illustrates the portion of the measuring apparatus
illustrated in FIG. 5 including a set of two wave shaping elements in a
second embodiment according to the invention;

[0083]FIG. 7 illustrates the portion of the measuring apparatus
illustrated in FIG. 5 including a set of two wave shaping elements in a
third embodiment according to the invention;

[0084]FIG. 8 is a plan view of the wave shaping elements shown in FIGS.
5, 6 and 7;

[0085]FIG. 9 illustrates the portion of the measuring system shown in
FIG. 6 including a set of five wave shaping elements in an arrangement
according to the invention;

[0086]FIG. 10 is a plan view of the wave shaping elements shown in FIG.
9;

[0087]FIG. 11 is a plan view of a set of nine wave shaping elements in an
arrangement according to the invention;

[0088]FIG. 12 illustrates a method, according to the invention, of
obtaining measurements by means of three sets of wave shaping elements
and stitching the measurement results;

[0089]FIG. 13 illustrates an arrangement of four wave shaping elements
with respect to an optical surface to be measured in an embodiment
according to the invention;

[0090]FIG. 14 is a plan view of the wave shaping elements shown in FIG.
13;

[0091]FIG. 15 illustrates an arrangement of two wave shaping elements
according to an embodiment of the invention;

[0092]FIG. 16 is a plan view of the wave shaping elements shown in FIG.
15;

[0093]FIG. 17 illustrates an arrangement of four wave shaping elements in
a further embodiment according to the invention;

[0094]FIG. 18 is a plan view of the wave shaping elements shown in FIG.
17;

[0095] FIG. 19 illustrates an arrangement of two wave shaping elements
with respect to a test object in a further embodiment according to the
invention;

[0096]FIG. 20 is a plan view of the wave shaping elements shown in FIG.
19;

[0097]FIG. 21 illustrates an arrangement of two wave shaping elements in
a further embodiment according to the invention;

[0098] FIGS. 22a to 22d are plan views of different arrangements of
diffractive measurement structures in further embodiments according to
the invention;

[0099] FIG. 23 is a plan view of two diffractive measurement structures in
an arrangement according to an embodiment of the invention;

[0100] FIGS. 24a to 24d illustrate sensitivity distributions related to a
first diffractive measurement structure according to FIG. 23;

[0101] FIGS. 25a to 25d illustrate sensitivity distributions related to a
second diffractive measurement structure according to FIG. 23;

[0102]FIG. 26 illustrates the shape of an optical surface of an asphere;

[0103]FIG. 27 illustrates the shape of an optical surface of a
double-asphere;

[0104] FIG. 28 shows a first embodiment of a projection objective
including at least one optical element in form of an asphere according to
the invention; and

[0105]FIG. 29 shows a second embodiment of a projection objective
including at least one optical element in form of an asphere according to
the invention.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

[0106] In the embodiments of the invention described below, components
that are alike in function and structure are designated as far as
possible by the same or like reference numerals. Therefore, in order to
fully understand the features of the individual components of a specific
embodiment, the descriptions of other embodiments or the summary of the
invention should be referred to.

[0107]FIG. 1 illustrates a measuring apparatus 10 in the form of an
interferometer system according to an embodiment of the invention. The
measuring apparatus 10 is used for interferometrically measuring a
deviation of an aspherical optical surface 12 of a test object 14. The
test object 14 can, for example, be a mirror or a transmissive optical
lens etc. The test object 14 is mounted on a test piece holder, not shown
in the drawings, which is rotatable about a rotational axis 16. The
optical surface 12 has, in the shown embodiment, a rotationally symmetric
shape about an axis of symmetry and the test object 14 is aligned and
mounted such that the axis of symmetry substantially coincides with the
rotational axis 16.

[0108] The measuring apparatus 10 comprises a light source unit 18 for
generating an illumination beam 20. The light source unit 18 comprises a
laser 19, such as a helium neon laser, emitting a laser beam 22. The
laser beam 22 is focused by a focussing lens 24 onto a pinhole aperture
of a spatial filter 26 such that a diverging beam 28 of coherent light
emerges from the pinhole. The wave front of the diverging beam 28 is
substantially spherical. The diverging beam 28 is collimated by a group
of lens elements 30 to form the illumination beam 20 having a
substantially flat wave front. The illumination beam 20 travels along an
optical axis 32 of the measuring apparatus 10 and traverses a beam
splitter 34. The optical axis 32 and the rotational axis 16 can be
identical as shown in FIG. 1, but do not have to be parallel or
identical.

[0109] In the following, the illumination beam 20 enters a Fizeau element
36 having a Fizeau surface 38. A portion of the light of the illumination
beam 20 is reflected as reference light 40 by the Fizeau surface 38. The
light of the illumination beam 20 traversing the Fizeau element 36 has a
plane wave front 42 and enters optional pre-shaping optics transforming
the light of the illumination beam into incoming light 46 having a
spherical wave front.

[0110] The measuring apparatus 10 further comprises a first wave shaping
element 48 and a second wave shaping element 50. The wave shaping
elements 48 and 50 are arranged in a so called cascaded arrangement. The
wave shaping elements 48 and 50 are shifted relative to each other both
along the optical axis 32 as well as in a direction perpendicular to the
optical axis 32. As shown in FIG. 5, the wave shaping elements 48 and 50
each comprise a diffractive measurement structure 52. The wave shaping
elements 48 and 50 are arranged in the above-mentioned cascaded manner
such that each of the diffractive measurement structures 52 is traversed
by a separate subset of rays of the incoming light 46 during operation of
the measuring apparatus 10. The diffractive measurement structures 52
each comprise a hologram, advantageously a computer generated hologram
(CGH). Such a hologram allows the wave front of the incoming light 46 to
be adapted to an aspherical shape.

[0111] The diffractive measurement structures 52 adapt the wave front of
respective portions of the incoming light 46 to respective portions of
the target shape of the optical surface 12. The wave front of the
incoming light 46 is thereby shaped by the diffractive measurement
structures 52 such that the light is orthogonally incident on the target
shape of the optical surface 12 at each location thereof. Thus, if the
optical surface 12 was precisely machined such that its surface shape
corresponded to the target shape, the incoming light 46 shaped by the
diffractive measurement structures 52 was orthogonally incident on the
optical surface 12 at each location thereof.

[0112] Light reflected from the optical surface 12, referred to as
measuring light 54, contains in its wave front the information on the
deviation of the actual shape of the optical surface 12 from the target
shape. As further shown in FIG. 1, the measuring light 54 then travels
back substantially the same way as the incoming light 46, traverses the
wave shaping elements 48 and 50, the pre-shaping optics 44, the Fizeau
element 36, and a portion of the measuring light 54 will be reflected by
the beam splitter 34. The measuring light 54 reflected by the beam
splitter 34 is imaged onto a photosensitive surface 56 of a camera chip
58 through an objective lens system 60 of a camera 62 such that the
optical surface 12 is imaged onto the camera chip 58.

[0113] A portion of the reference light 40 is also reflected by the beam
splitter 34 onto the photosensitive surface 56 of the camera chip 58. The
reference light 40 and the measuring light 54 generate an interference
pattern on the photosensitive surface 56. The measuring apparatus 10
further comprises evaluation means 64, which are adapted for determining
the deviation distribution of the optical surface 12 from the target
shape based on the measured interference pattern.

[0114] FIGS. 2 and 3 show further embodiments of a portion of the
measuring apparatus 10 arranged in the right section of FIG. 1. In the
embodiment shown in FIG. 2, the propagation direction of the illumination
beam 20 is tilted by a prism 66 such that the incoming light 46 is not
directly orthogonally incident on the wave shaping elements 48 and 50.
This way, reflexes disturbing the interferometric measurement are
avoided. The wave shaping elements 48 and 50 in FIGS. 2 and 3 are shown
in a schematic way and their arrangement as well as structure can be any
of the embodiments illustrated herein.

[0115] In the embodiment shown in FIG. 3 a negative F-aplanar 68 is
provided to transform the illumination beam 20 into a diverging beam of
the incoming light 46. The optical axis 32 of the measuring apparatus 10
is shifted with respect to the rotational axis of the test object 14. In
this way, errors of the diffractive measurement structures 52 are
averaged out during the interferometric measurement at different
rotational positions of the test object 14.

[0116]FIG. 4 illustrates single rays of the measuring light 54 reflected
by an embodiment of the optical surface 12 having an aspherical concave
shape. The term "concave", as used in this application with respect to
the optical surface 12, refers to a viewing direction along the
propagation direction of the incoming light 46. The same applies to the
use of the term "convex" with regards to the optical surface 12. As shown
in FIG. 4, there is an area, referred to as "caustic area" 70, located a
certain distance away from the test object 14, in which at least two rays
of the measuring light 54 intersect with each other. Before and after the
caustic area 70 with respect to the optical axis 32 so called unambiguous
areas 72 and 74 are located, in which no single rays of the measuring
light 54 intersect with each other. In case the wave shaping elements 48
and 50 are located in the "caustic area" 70 the measurement is
indeterminate.

[0117] The wave shaping elements 48 and 50 therefore have to be located in
one of the unambiguous areas 72 and 74 to allow for a meaningful
measurement. In case of the wave shaping elements 48 and 50 being
arranged in the unambiguous area 74, located between the "caustic area"
70 and the test object 14, the size of the diffractive measurement
structures 52 have to be on the order of the size of the optical surface
12.

[0118]FIG. 5 shows a portion of the measuring apparatus designated as "V"
in FIG. 1. The wave shaping elements 48 and 50 overlap in projection
along the optical axis 32. In this area of overlap the second wave
shaping element 50 comprises a first diffractive alignment structure 76
in the form of a computer generated hologram (CGH) which is adapted for
focussing a portion of the incoming light 46 onto a reflective surface 78
on the first wave shaping element 48. The first diffractive alignment
structure 76 thereby generates a spherical auxiliary wave 80 which
focuses onto the reflective surface 78. Such a focusing condition is also
referred to as a cat-eye focus condition.

[0119] The light reflected from the reflective surface 78 forms an
interference pattern with the reference light 40 on the photosensitive
surface 56 of the camera chip 58. This interference pattern is indicative
of a distance between the two wave shaping elements 48 and 50 with
respect to the surface normal of element 50. Therefore, the first
diffractive alignment structure 76 allows the distance between the wave
shaping elements 48 and 50 to be measured and subsequently to be
adjusted. The second wave shaping element 50 further comprises a second
diffractive alignment structure 82 acting as a Littrow grating. The
second diffractive alignment structure 82 is arranged on a radially outer
area of the second wave shaping element 50 with respect to the optical
axis 32. The second diffractive alignment structure 82 allows measurement
and adjustment of the tilt angle of the second wave shaping element 50
with respect to the optical axis 32. Also the first wave shaping element
48 comprises a diffractive alignment structure 84 acting as a Littrow
grating which allows the tilt angle of the first wave shaping element 48
with respect to the optical axis 32 to be measured and adjusted.

[0120] Further, the wave shaping elements 48 and 50 can contain further
diffractive structures (not shown in the drawings) to control the
geometrical arrangement of the wave shaping elements 48 and 50 relative
to the measuring apparatus 10 and to control the geometrical arrangement
of the optical surface 12 of the test object 14 relative to the
combination of the wave shaping elements 48 and 50 as described in the
U.S. patent application Ser. No. 11/233,435.

[0121] The wave shaping elements 48 and 50 of the embodiment shown in FIG.
6 differ from the wave shaping elements 48 and 50 according to FIG. 5 as
follows. The first diffractive alignment structure 176 of the second wave
shaping element 50 according to FIG. 6 has a different function than the
first diffractive alignment structure 76 according to FIG. 5, and the
first wave shaping element 48 according to FIG. 6 comprises two
diffractive alignment structures 178 and 84 acting as Littrow gratings.
The diffractive alignment structure 84 is, as in the embodiment according
to FIG. 5, used for adjusting the tilt angle of the first wave shaping
element 48 with respect to the optical axis 32.

[0122] The first diffractive alignment structure 176 transforms a portion
of the incoming light 46 into a converging spherical auxiliary wave 180
having its focus between the first diffractive alignment structure 176 of
the second wave shaping element 50 and the diffractive alignment
structure 178 of the first wave shaping element 48. The light of the
auxiliary wave 180 reflected back by the diffractive alignment structure
178 acting as a Littrow grating interferes with the reference light 40 on
the photosensitive surface 56 of the camera chip 58.

[0123] The resulting interferogram is indicative of the distance between
the wave shaping elements 48 and 50 with respect to the surface normal of
element 50 as well as a decentration of the wave shaping elements 48 and
50 relative to each other in a direction perpendicular to the surface
normal of element 48. Therefore, according to the embodiment shown in
FIG. 6 the distance between the wave shaping elements 48 and 50, their
relative decentration and their tilt angle with respect to each other can
be determined and appropriately adjusted during the alignment process.
Further, the Littrow structures 82 and 84 are used to determine the tilt
with respect to the optical axis 32.

[0124] The embodiment according to FIG. 7 differs from the embodiment
according to FIG. 6 in that the second wave shaping element 50 comprises
a first diffractive alignment structure 276 which differs from the first
diffractive alignment structure 176 according to FIG. 6 in that it
contains partial alignment structures 86 and 88.

[0125] Further, the first wave shaping element 48 is provided with a first
diffractive alignment structure 278 located next to a reflective surface
279. The first partial alignment structure 86 generates an auxiliary wave
280 from the incoming light 46, which auxiliary wave 280 has a
propagation direction tilted with respect to the optical axis 32. The
auxiliary wave 280 is reflected by the first diffractive alignment
structure 278 acting as a Littrow grating.

[0126] The reflected light interferes with the reference light 40 on the
photosensitive surface 56 of the camera chip. The resulting interferogram
is indicative of the lateral position of the two wave shaping elements 48
and 50 relative to each other with respect to the surface normal. The
second partial alignment structure 88 focuses the incoming light 46 onto
the reflective surface 279 and allows analogously to the first
diffractive alignment structure 76 according to FIG. 5 the measurement of
the distance between the two wave shaping elements 48 and 50. According
to the embodiment shown in FIG. 7, the axial and lateral distance of the
wave shaping elements 48 and 50 relative to each other as well as the
tilt angles of the wave shaping elements 48 and 50 with respect to each
other can be measured in correspondence to FIG. 6.

[0127]FIG. 8 shows the positioning of the wave shaping elements 48 and 50
with respect to the optical surface 12 to be measured in a view along
axis 16. In order to measure the entire optical surface 12, the test
object 14 is rotated around the rotational axis 16 and measurements are
performed at various rotational positions. The measurement results for
the different rotational positions are subsequently mathematically
stitched, as explained later, to obtain a measurement result of a
deviation distribution of the entire optical surface from its target
shape.

[0128] FIGS. 9 and 10 illustrate a further embodiment of the measuring
apparatus 10 according to the invention. The measuring apparatus 10
according to this embodiment differs from the embodiment shown in FIG. 1
in that it comprises a larger number of wave shaping elements 48 and 50.
Specifically, three first wave shaping elements 48 are arranged in a
first common plane. Two second wave shaping elements 50 are arranged in a
second common plane such that the second wave shaping elements 50 cover
gaps between the first wave shaping elements 48. The alignment between
wave shaping elements 48 and 50 can be achieved according to any of the
variations shown in FIGS. 5 to 7. In the embodiment according to FIGS. 9
and 10 the wave shaping elements 48 and 50 are arranged along an axis
perpendicular to the optical axis 32 (z-axis). FIG. 11 illustrates a
further embodiment of the invention, in which the wave shaping elements
48 and 50 are arranged in two directions perpendicular to the optical
axis 32 (x- and y-axes). For an optical surface 12 being rotationally
symmetric about the rotational axis 16 the entire optical surface 12 can
be measured by the embodiments of the measuring apparatus illustrated in
FIGS. 5 to 11. For this purpose respective portions of the optical
surface 12 are measured at different rotational positions of the optical
surface 12 and thereafter the measurement results are stitched together
mathematically.

[0129]FIG. 12 shows a further embodiment of the invention, according to
which a rotationally non symmetric optical surface 12, that means a so
called free form surface, can be measured. According to this embodiment
respective portions of the optical surface 12 are consecutively measured
using three different sets of wave shaping elements. In a first
measurement step, a measurement is made using a first set of wave shaping
elements 282a. Set 282a comprises four first wave shaping elements 48a
arranged in a spaced even arrangement in a first plane. Second wave
shaping elements 50a are arranged in a second plane such that they
overlap somewhat with the first wave shaping elements 48a in projection
along the optical axis 32 in order to allow alignment between the wave
shaping elements 48a and 50a according to the invention. Further, third
wave shaping elements 51a are arranged in a third plane such that they
overlap somewhat with the first wave shaping elements 48a and the second
wave shaping elements 50a in projection along the optical axis 32 in
order to allow alignment of the wave shaping elements 51a to the wave
shaping elements 50a and/or the wave shaping elements 48a. The wave
shaping elements 48a, 50a and 51a comprise respective diffractive
measurement structures 52, each being correspondingly adapted to the
target shape of the optical surface 12 in a respective area.

[0130] Further, a second set 282b of wave shaping elements and a third set
282c of wave shaping elements are provided each having the same basic
arrangement structure as the first set 282a. The respective overall
arrangements of the sets 282a, 282b and 282c are, however, shifted
relative to each other in a plane perpendicular to the optical axis 32.
Different areas of the optical surface 12 are covered by the respective
diffractive measurement structures 52, such that the entire optical
surface 12 is covered by the diffractive measurement structures 52 of all
three sets 282a, 282b and 282c. The respective diffractive measurement
structures are individually adapted to the respective portions of the
optical surface 12 covered by the same. The measurement results obtained
by the three sets 282a, 282b and 282c are stitched together using
mathematical stitching methods. In the embodiment of FIG. 12 the three
sets of wave shaping elements 282a, 282b and 282c are replaced by each
other for the different measurements. In a further embodiment the
different measurements are conducted by three different interferometric
measuring apparatuses 10. Therefore the different measurements can be
conducted using an incoming light beam 46 from a single interferometer or
from respective illumination beams of separate interferometers.

[0131] FIGS. 13 and 14 show a further embodiment of an arrangement of wave
shaping elements 284 together with an optical surface 12 to be measured.
In this embodiment four wave shaping elements 284 are arranged next to
each other in an overlapping manner, such that each of the four quadrants
of the optical surface 12 is covered by a respective wave shaping element
284. In case of the optical surface 12 to be measured being convex, as
displayed in FIG. 13, the required size of the wave shaping elements 284
is determined by the diameter D as well as the radius of curvature R of
the optical surface 12. Given a constant diameter Dds covered by the
diffractive measurement structures 52 of the wave shaping elements 284,
the maximum diameter D of the optical surface 12 testable is defined by:

D = 2 R sin { arctan D ds 2 R ds }
, ( 5 ) ##EQU00007##

wherein Rds is the maximum distance between the wave shaping
elements 284 and the center of curvature of the optical surface 12.

[0132] The maximum diameter of a single CGH acting as the diffractive
measurement structure 52 currently available in appropriate quality is
smaller than 300 mm. The optical surface 12 shown in FIG. 13 is
aspherical in shape, that means it departs slightly from a spherical
shape. This is schematically illustrated in FIG. 26. Therein, a best
fitting sphere 286 of the optical surface 12 is shown. The best fitting
sphere 286 has the radius of curvature R and the diameter D. The actual
optical surface of the test object 14 deviates from the best fitting
sphere 286 by a maximum of Δ. The proportion of the deviation
Δ with respect to the radius of curvature and the diameter D is
exaggerated in FIG. 26 for illustrative purposes. FIG. 27 shows a test
object 14 in the form of a double-asphere.

[0133] FIGS. 15 and 16 show a further embodiment of an arrangement of two
wave shaping elements 284a and 284b according to the invention. Each of
the wave shaping elements 284a and 284b comprises a respective
diffractive measurement structure 52a and 52b. Each of the diffractive
measurement structures 52a and 52b has a respective surface normal 288a
and 288b. The wave shaping elements 284a and 284b are tilted relative to
each other such that the respective surface normals 288a and 288b are
also tilted relative to each other by a tilt angle α.

[0134] In the shown example, the tilt angle α is around 15°.
Therefore, the diffractive measurement structures 52a and 52b form a
"roof"-shaped structure into which the optical surface 12 is partly
inserted. This way the diffractive measurement structures 52a and 52b
follow in a first approximation the shape of the optical surface 12 which
allows an optical surface 12 having a larger diameter D to be measured as
compared to the embodiment according to FIG. 13 using diffractive
measurement structures of the same size.

[0135]FIG. 16 is a plan view of the wave shaping elements 284a and 284b
of FIG. 15 viewed in a direction of the incoming light 46. As is apparent
from FIG. 16 the wave shaping element 284b covers the central area of the
optical surface 12 containing the rotational axis 16. For measuring the
entire optical surface 12 the optical surface 12 is rotated and
measurements are taken at several rotational positions. According to one
embodiment the wave shaping elements 284a and 284b are aligned relative
to each other using the alignment structures illustrated in FIGS. 5 to 7.

[0136] FIGS. 17 and 18 show an arrangement of four wave shaping elements
284a, 284b, 284c and 284d in an embodiment according to the invention,
which allows the measurement of a free form optical surface 12. According
to this embodiment the wave shaping elements 284a, 284b, 284c and 284d
are arranged to form a four sided roof. That means, the wave shaping
elements 284a, 284b, 284c and 284d are arranged next to each other in
order to cover all four quadrants of the optical surface 12, wherein the
respective wave shaping elements are each tilted relative to their
neighbouring wave shaping elements.

[0137] FIGS. 19 and 20 illustrate a further embodiment of the wave shaping
elements 284a and 284b. According to this embodiment the wave shaping
elements 284a and 284b are adapted for measuring a test object 14, which
is rotationally symmetric with regards to a rotational axis 290. The
rotational axis 290 is arranged perpendicular to the propagation
direction of the incoming light 46. During measurement the test object 14
is measured in different rotational positions around the rotational axis
290 and the measurement results are stitched together mathematically.

[0138]FIG. 21 illustrates a further embodiment of a measuring apparatus
according to the invention, in which the incoming light 46 comprises two
incoming light beams 292a and 292b, each of which is nearly perpendicular
to a respective wave shaping element 284a and 284b arranged in a tilted
fashion. The separate incoming light beams 292a and 292b can originate
from a single interferometer or from the respective illumination beams of
separate interferometers. According to this embodiment a larger surface
area of the optical surface 12 can be measured.

[0139] FIGS. 22a to 22d show different arrangements of diffractive
measurement structures 52 suitable for performing a further embodiment of
the measuring method according to the invention, which measuring method
includes a stitching algorithm for adjusting misalignments between single
diffractive measurement structures 52. According to this measuring method
an optical surface being rotationally symmetric with respect to a
rotational axis 16 is rotated into different rotational positions and the
wave front of the respective measuring light 54 is measured accordingly.
In the arrangements according to FIGS. 22b and 22c a central diffractive
measurement structure is provided in the centre of the optical surface
12. In the arrangements according to FIGS. 22a and 22d the diffractive
measurement structures are arranged such that the area of the rotational
axis 16 on the optical surface 12 is covered by an outer area of one of
the diffractive measurement structures 52.

[0140] In an embodiment of the measuring method according to the
invention, the diffractive measurement structure 52 covering the
rotational axis 16 is first roughly aligned, for example by means of an
optical coherence tomography (OCT) distance measuring system, a Littrow
grating and/or an autocollimator. Subsequently, the test object 14 is
inserted into the measuring apparatus 10 and the test object 14 and the
central diffractive measurement structure 52 are alternately aligned.
Subsequently, the remaining diffractive measurement structures 52 which
do not cover the rotational axis 16 are roughly aligned, either optically
or by means of CGH-alignment structures. This rough alignment has the
purpose of minimising the wave front error of the measuring light 54 such
that a continuous wave front within the single measurement structures 52
can be measured from the light originating from each diffractive
measurement structure 52.

[0141] The embodiment of the measurement method according to the invention
further comprises the step of arranging the optical surface 12 in a first
rotational position, and illuminating a first area of the optical surface
12 with the incoming light 46 having traversed the respective diffractive
measurement structures 52 whereby a first measuring light having
interacted with the first area is generated.

[0142] Subsequently, the wave front of the first measuring light is
determined interferometrically by superimposing the first measuring light
with the reference light 40. Afterwards the test object 14 is rotated
into a second rotational position and a second area of the optical
surface, which partially overlaps with the first area, is illuminated
with the incoming light having traversed the diffractive measurement
structures 52 and thereby first measuring light having interacted with
the second area is generated. Thereafter, the wave front of the second
measuring light is determined interferometrically. The above steps are,
if necessary optionally repeated with the test object 14 being arranged
in further rotational positions. The number of rotational positions has
to be chosen so that the complete optical surface can be stitched from
the measured wave fronts.

[0143] Further, sensitivity distributions (Bkl)x,y,rotn for each
diffractive measurement structure 52 are determined, which sensitivity
distributions (Bkl)x,y,rotn describe the influence of a given
misalignment of a respective diffractive measurement structure k in a
respective degree of freedom l on a wave front related to a given
rotational position rotn of the optical surface 12. The influence on the
wave front is described as a function of the coordinates x and y
orthogonal to the propagation direction of the measuring light 54 or the
optical axis 32. In other words, the sensitivity distribution
(Bkl)x,y,rotn describes an effect to the wave front of the
measuring light 54 caused by an alteration of the position of the
respective diffractive measurement structure 52 in a given degree of
freedom l. The degrees of freedom l for a single diffractive measurement
structure 52 include tilt x, tilt y, decentration x, decentration y,
azimuthal angle and distance z.

[0144]FIG. 24a shows an example of a sensitivity distribution
(B11)x,y for a first diffractive measurement structure 52a
according to FIG. 23 in a second rotational position, in which the
optical surface 12 is rotated form a first rotational position shown in
FIG. 23 clockwise by 60°. This sensitivity distribution shows the
effect of a variation of the distance z between the diffractive
measurement structure 52a and the neighboring diffractive measurement
structure 52b on the wave front distribution of the measuring light 54.
FIG. 25b shows the sensitivity distribution (B12)x,y describing
the effect of varying the position of the diffractive measurement
structure 52a along the x-axis. FIGS. 24c and 24d depict the sensitivity
distributions (B11)x,y and (B12)x,y with the optical
surface 12 being rotated back to the first rotational position of the
optical surface 12 shown in FIG. 23. In analogy to FIGS. 24a to 24d,
FIGS. 25a to 25d show sensitivity distributions of a second diffractive
measurement structure 25b according to FIG. 23.

[0145] According to the inventive method misalignment coefficients in the
form of fitting coefficients amj and bkl are determined by
minimizing the following term:

wherein: ACGHs is the number of single diffractive measurement structures
52 in form of CGHs, Af is the number of degrees of freedom in alignment
of the single diffractive measurement structures 52 (usually six degrees
of freedom: tilt x, tilt y, decentration x, decentration y, azimuth angle
and distance z); (Bkl)x,y,rotm is the distribution for a degree
of freedom l of the k-th diffractive measurement structure rotated back
to the angle of the m-th rotational position at the surface coordinate x,
y. The rotation also includes a distortion correction. bkl is the
fitting coefficient of the sensitivity distribution of the l-th degree of
freedom of the k-th diffractive measurement structure; AD is the number
of rotational positions; Wm x,y is the wave front in the m-th
rotational position, rotated back to the angle of the m-th rotational
position at the surface coordinate x,y; AJ is the number of degrees of
freedom in alignment of the optical surface 12 (usually five degrees of
freedom: tilt x, tilt y, decentration x, decentration y and distance z
with respect to measuring apparatus 12). Aj x,y is the sensitivity
distribution for a degree of freedom j of the optical surface 12 at the
surface coordinate x,y; aij is the fitting coefficient of the
sensitivity distribution for the j-th degree of freedom of the optical
surface 12 for the i-th rotational position;

[0146] The sensitivity distribution Aj x,y describes the influence of
a given misalignment of the optical surface 12 in a respective degree of
freedom j on the wave front of the measuring light 54 as a function of
the coordinates x and y, and amj and anj are misalignment
coefficients in the form of fitting coefficients of the optical surface
12 for respective rotational positions m and n.

[0147] The fitting coefficients amj and bkl are determined from
the above least square approach by determining the derivative of equation
(6) with respect to the single coefficients amj and bkl and
determining the solution of the linear system of equations resulting
therefrom. For determining the wave front Wm interferometer errors
should be considered after the measurement (depending on the arrangement,
for example, wave front errors through the Fizeau surface 38, a prism and
above all the effect of the single diffractive measurement structures
(disturbance data), which are determined during qualification of the
diffractive measurement structures 52).

[0148] The determined fitting coefficients amj and bkl are
combined with the measured wave fronts Wm and an overall deviation
distribution of the optical surface 12 from the target shape is
determined therefrom.

[0149] Referring to FIG. 26 an optical element in the form of an asphere
14 is provided according to the invention. The asphere 14 has an
aspherical optical surface 12 extending over a diameter D of the asphere.
According to a first embodiment a best fitting spherical surface 286 of
the aspherical optical surface 12 has a radius of curvature R, and the
parameters D and R are related as follows:

D > 2 R sin ( arctan 500 mm 2 R
) ( 7 ) ##EQU00009##

[0150] According to a second embodiment of the asphere a best fitting
spherical surface of the aspherical optical surface has a radius of
curvature R of at least 130 mm, and the ratio D/R is larger than 1.3. In
further variations the ratio D/R is larger than 1.5, especially larger
than 2.0.

[0151] The manufacture of such such an asphere either according to the
first embodiment or the second embodiment is made possible by the
manufacturing method according to the invention as explained above in
more detail.

[0152] The asphere 14 according to the first or the second embodiment can
be configured as a lens or a mirror, especially for use in a projection
exposure tool for microlithography. In an embodiment the asphere 14 is
configured as a mirror used in a projection objective of a projection
exposure tool for microlithography operating with extreme ultraviolet
light (EUV), e.g. light having a wavelength of 13.4 nm. Embodiments of
such a projection objective are presented below in detail.

[0153] The best fitting aspherical optical surface 12 can be convex or
concave. In one variation the diameter D is larger than 500 mm. In a
further variation the optical surface 12 is rotationally non-symmetric
and diameter D is larger than 300 mm. The optical surface can have a
deviation from said best fitting spherical surface of at least 50 μm,
in particular at least 100 μm or at least 200 μm. The actual shape
of said optical surface deviates from a target shape of the optical
surface by a maximum of 5 μm.

[0154] FIG. 28 shows a first exemplary embodiment 1000 of a projection
objective for a projection exposure tool operating with EUV-radiation.
The projection objective 1000 according to FIG. 28 includes six
rotationally-asymmetric mirrors 1310, 1320, 1330, 1340, 1350, and 1360.
An asphere of the above described type according to the invention is used
as at least one of these mirrors, which is manufactured, e.g. using the
manufacturing method according to the invention. That means at least one
of the mirrors is an asphere according to the invention.

[0155] The projection objective 1000 images EUV-radiation from an object
plane 1103 to an image plane 1102 along a reference axis 1105. Data for
the projection objective 1000 is presented Table 1A and Table 1B below.
Table 1A presents optical data, while Table 1B presents
rotationally-asymmetric constants for each of the mirror surfaces. For
the purposes of Table 1A and Table 1B, the mirror designations correlate
as follows: mirror 1 (M1) corresponds to mirror 1310; mirror 2 (M2)
corresponds to mirror 1320; mirror 3 (M3) corresponds to mirror 1330;
mirror 4 (M4) corresponds to mirror 1340; mirror 5 (M5) corresponds to
mirror 1350; and mirror 6 (M6) corresponds to mirror 1360. "Spacing" in
Table 1A refers to the distance between adjacent elements in the
radiation path. The monomial coefficients Cj, for the
rotationally-asymmetric mirrors, along with the amount the mirror is
decentered and rotated from an initial projection objective design, are
provided in Table 1B. R, the basic radius, is the inverse of the vertex
curvature c. Decenter is given in mm and rotation is given in degrees.
Units for the monomial coefficients are mm-j+1. Nradius is a
unitless scaling factor. In FIG. 28, the projection objective 1000 is
shown in meridional section. The meridional plane is a symmetry plane for
projection objective 1000. Symmetry about the meridional plane is as the
mirrors are decentered only with respect to the y-axis and tilted about
the x-axis. Further, the coefficients for the rotationally-asymmetric
mirrors having an odd degree in the x-coordinate (e.g., x, X3,
x5, etc.) are zero.

[0156] The projection objective 1000 is configured for operation with 13.5
nm radiation and has an image-side NA of 0.35 and a tracklength of 1,500
mm. The optical path length of imaged radiation is 3,833 mm. Accordingly,
the ratio of optical path length to tracklength is approximately 2.56.
The projection objective has a demagnification of 4×, a maximum
distortion of less than 100 nm, Wrms of 0.035λ, and a field
curvature of 28 nm.

[0157] For the mirrors in projection objective 1000, the maximum deviation
of the rotationally-asymmetric surfaces from a corresponding spherical
rotationally-symmetric reference surface for each mirror is as follows:
154 μm for mirror 310; 43 μm for mirror 320, 240 μm for mirror
330; 1,110 μm for mirror 340; 440 μm for mirror 350; and 712 μm
for mirror 360. The maximum deviation of the rotationally-asymmetric
surfaces from a corresponding aspherical rotationally-symmetric reference
surface is 47 μm for mirror 310; 33 μm for mirror 320, 96 μm for
mirror 330; 35 μm for mirror 340; 152 μm for mirror 350; and 180
μm for mirror 360.

[0158] The first and second mean curvature for mirror 310 are
9.51×10-4 and 9.30×10-4 respectively. Respective
first and second mean curvatures for the other mirrors in the projection
objective 1000 are as follows: 2.76×10-5 and
1.56×10-5 for mirror 1320; -2.38×10-3 and
-2.17×10-3 for mirror 1330; 1.79×10-3 and
1.75×10-3 for mirror 1340; -2.64×10-3 and
-2.10×10-3 for mirror 1350; and 1.93×10-3 and
1.91×10-3 for mirror 1360. The sum of the first mean curvature
for projection objective 1000 is -3.19×10-4. The sum of the
second mean curvature is 3.29×10-4. The sum of the first and
second mean curvatures is 9.97×10-6 and the inverse sum of the
first and second mean curvatures is 1.00×10-5.

[0159] The projection objective 1000 images radiation from object plane
1103 to an intermediate image at a location 1305 near mirror 1360.
Embodiments that have one or more intermediate images, also include two
or more pupil planes. In some embodiments, at least one of these pupil
planes is physically accessible for the purposes of placing an aperture
stop substantially at that pupil plane. An aperture stop is used to
define the size of the projection objective's aperture.

[0160]FIG. 29 shows a second exemplary embodiment of a projection
objective 2000 for an projection exposure tool operating with
EUV-radiation. The projection objective 2000 includes four
rotationally-asymmetric mirrors 2310, 2320, 1230, and 2340, which direct
radiation from an object plane 2103 to an image plane 2102. An asphere of
the above described type according to the invention is used as at least
one of these mirrors, which is manufactured, e.g. using the manufacturing
method according to the invention. The projection objective 2000 images
radiation from an object plane 2103 to an image plane 2102 with a
demagnification ratio of 4×.

[0161] The projection objective 2000 has an image-side NA of 0.26 and has
a rectangular field. The height and width of the field at object plane
2102 is 8 mm and 100 mm, respectively. The tracklength of the projection
objective 2000 is 2,360 mm. The image plane 2102 is tilted with respect
to object plane 2103 by -3.84°.

[0163] With respect to Table 2D, xObject/mm and yObject/mm
denote the x- and y-coordinates in the object plane. The values
Distortion(x)/nm and Distortion(y)/nm denote the distortion at the
respective coordinate. Absolute Value of Distortion/nm denotes the
absolute distortion value at the respective coordinate.
Telecentricity/Degrees denotes the chief ray angle at the respective
coordinate. Wavefront Error at 13.5 nm denotes the RMS wavefront error in
units of the illumination wavelength λ=13.5 nm. As the optical
system is mirror symmetric with respect to the yz-plane it is sufficient
to give data for fieldpoints having positive x-coordinates in the object
plane.

[0164] Further details regarding the projection objectives shown in FIGS.
28 and 29 can be taken from US 2007/0058269 A1, the entire content of
which is hereby incorporated by reference. The optical element according
to this invention can also be included in further embodiments of
projection objectives described in this reference.

[0165] While the invention has been described with respect to a limited
number of embodiments and applications, it will be appreciated that many
variations, modifications and other applications of the invention may be
made. The applicant seeks, therefore, to cover all such variations,
modifications and other applications as fall within the spirit and scope
of the invention, as defined by the appended claims, and equivalents
thereof.